Aircraft: B737
Phase of flight: Descent
Anomaly: Deviation - Track / Heading All Types; Deviation / Discrepancy - Procedural Published Material / Policy; Deviation / Discrepancy - Procedural Clearance

Captain was new on the airplane (coming off 757 First Officer seat) and new in the left seat with approx. 35 hours. Flew arrival into SLC. Captain stated he had a few questions about how VNAV would work in reference to altitudes. We discussed his questions. Captain stated that he did not think that was how the VNAV and the FMC worked and made references to the 757 FMC and how it was smarter. ATC gave us a standard published altitude crossing; we started down in VNAV. In the descent ATC cleared us to 'descend to 11;000 feet'. 11;000 was set in the MCP. We both pointed and he repeated it back. There was a 13;000 hard altitude restriction in the FMC. I asked the Captain if he wanted me to remove it from the box. He said no. I asked him if he wanted level change or altitude intervention. He said no. I asked him if he understood the clearance and that it was a descent to and not a descend via. He said he understood and repeated it back and pointed again at the MCP. I told him the aircraft would level at 13;000 feet; and that that was not our clearance. He said he wanted to see if it was smart enough to go down to 11;000 feet. I pulled up the VSI and showed him that it would level at 13;000 feet and continue to stay level until it reached the top of descent point to make the 11;000 feet restriction. He said it should go down. I explained to him it wouldn't. He said he thought I was wrong and just needed to see it for himself. I said Ok; we will let it go until it starts to level off at 13;000 feet but then we need to get it down to 11;000 feet so we don't get violated. The airplane leveled at 13;000 feet as advertised. He said it was an 'FMC anomaly just like the 75'. I told him it was not an anomaly and it was working fine and to start down. He said no let's see if it can fix itself. I said there is nothing wrong with it; start down! He said the FMC doesn't know what to do; because it does not have smart enough software. I said we need to start down. I announced that I would help him and I pushed level change button and annunciated the selection. The airplane started down. He said he did not want to go down that fast and he would use vertical speed. He reached up and pushed the 'approach button' by mistake instead of vertical speed. He then tried to use the thumb wheel and said 'see it doesn't work; I told you so; the FMC is broken and there is something wrong with MCP.' He announced he was going to hand fly it and clicked the autopilot off. He continued straight ahead and pulled up comfortably putting the airplane into a slight climb. I told him he needed to descend and to get down to 11000 feet ASAP. He started to descend but continued straight during the process. I told him to come right he was no longer on the arrival track which turned to the right. He did not. Approach control said we were not on the track and asked if we were having navigation problems. I said no NAV problems; and he told us to turn right to heading of 190 degrees. I replied and set 190 on the MCP and selected Heading select. It did not work because the airplane had now captured the approach mode. The Captain turned left instead of right. I reached up to turn off the flight directors and I heard bank angle. The aircraft was near 40 degrees bank. I told the Captain to lessen the bank and I helped by giving a small upward push on the left side of the yoke. The controller said we were going farther left and to turn right to a heading of 230. I replied and let go of the yoke to set the heading on the MCP and we got another bank angle warning. I came back to the yoke and announced I was coming on the controls and to turn right. The Captain said 'see I told you now the whole mode control panel is not working.' I told him we were level at 11000 feet; autopilot was off and to just stay in 30 degrees of bank and fly a heading off the compass. He turned to a heading of 230. The controller asked again if we had a problem with our navigation. I said 'no; the Captain wasnew in the aircraft and pushed a wrong button'; and that we were correcting and apologized. I put the autopilot back on for him and verbalized it. The Controller gave us radar vectors for an ILS 34L. We flew a normal approach and landing. At the gate we discussed what happened. The Captain said he still thought the airplane was not working. I told him there was nothing wrong with the aircraft. He said 'Then how do you explain ...' I explained each part of what happened and why it happened in reference to the FMC; VNAV and the mode control panel. He said thanks and apologized. I then asked him questions. I asked him if he heard and understood the clearance to 11;000 feet. He said yes. I asked him if he understood that it was descend to and not descend via. He said yes. I asked him if he heard me tell him at least 5 times if not more that we needed to descend. He said yes. I asked him why he didn't listen to me and descended. He replied; because he knew that 'he was right!' I told him to be a successful Captain; it was a crew airplane and that he needed to accept input from the Copilot and use CRM skills. I told him I thought he had vertigo or his head was not on straight because he had mentioned he was getting a cold and his sinuses were bothering him and he kept rolling into a steep bank. He said his head was fine and that he rolled into 40 degrees of bank on purpose to correct faster. I told him we are not allowed to normally use 40 degrees bank and that it was not a good idea to do that in the weather; with no Situational Awareness; and without announcing it to the other pilot. He did not reply. B737 First Officer describes an arrival during which a new Captain; also new to the B737; experiments with the FMC and MCP much to the chagrin of the First Officer; resulting in track deviations that are detected by ATC and vector headings are issued.